FUNDAMENTALS OF ALGEBRA 2A CHAPTER 10 POWERPOINT PRESENTATION

TRIGONOMETRY

TRIGONOMETRY

LEARNING TARGETS

• AFTER YOU COMPLETE THIS CHAPTER, YOU WILL BE ABLE TO:

• DEFINE TRIGONOMETRIC RATIOS• CHANGE MEDIAN MEASURE TO DEGREE

MEASURE• DEFINE AND NAME TRIGONOMETRIC RATIOS IN

SPECIAL TRIANGLES• IDENTIFY GRAPHS OF SINE, COSINE, & TANGENT• USE THE LAW OF SINES AND COSINES

TRIGONOMETRY RATIOS

• Trigonometry: Comes from the Greek word, “trigonon” or triangle and “metron” to measure. The main part of trigonometry is the right triangle. There are several special names that define the ratios.

• Cosine, Sine, and Tangent.• They also have reciprocals (or the opposite)

Here is a chart of the ratios…..

Here is a list of reciprocal ratios…

Chapter Vocabulary• Degree: 1/360 of a full circle – symbol = ⁰• Minute: 1/60 of a degree, so 1⁰ = 60’• Second: 1/60 of a minute, so 1’ = 60”• Quadrant – four parts of a circle, using Roman Numerals

and numbers counter-clockwise.• Quadrant I = 0⁰ to 90⁰• Quadrant II = 90⁰ to 180⁰• Quadrant III = 180⁰ to 270⁰• Quadrant IV = 270⁰ to 360⁰

What does this look like?

• Radians – the angle between two radii of a circle, which is cut off on the circumference by an arc equal in length to the radius.

A 360⁰ Circle

Special Triangles

• 30 – 60 – 90 Triangle• 45 – 45 – 90 Triangle• There is a unique relationship to the sides in

these triangles:

Basic Identities

• Reciprocal – opposites• Pythagorean – using Pythagorean Theorem• Quotient – using division• Cofunction – one ratio working with another

Reciprocal Identities

Pythagorean Identities

Quotient Identities

Cofunction Identities

Other Identities

The Unit Circle

• In the unit circle – the radius is 1. The right triangle for each quadrant is determined by the reference angle, the angle with the initial side at 0⁰.

Inverse Trigonometric Functions

• A quick look at the graph for cosine, sine, and tangent shows that there is one x and y value. They can pass the vertical line test. The inverse or opposite function cannot.

• Principal value: The value of a function in a restricted range.

• Arcsin, Arccos, Arctan are the inverse functions.

COSINE CURVE

SINE CURVE

TANGENT CURVE

COFUNTCIONS AND COMPLEMENTARY ANGLES

• COFUNCTIONS OF COMPLETMENTARY ANGLES ARE EQUAL.

• COFUNTCION PAIRS:

SOLVING THE TRIANGLE

• Solving the triangle: the process to find the missing sides and angles.

• Law of Sines:

Law of Cosines – Arbitrary Triangles